If n(A ∩ B) = 0, n(A) = 28, and n(B) = 34, what is n(A △ B)?
Answer and explanation
Correct answer: 62
The symmetric difference A △ B contains elements that belong to exactly one of the two sets. Its cardinality is n(A △ B) = n(A) + n(B) − 2n(A ∩ B). Since the intersection has size zero, the sets are disjoint and n(A △ B) = 28 + 34 − 0 = 62. Options 28 and 34 count only one set, while 6 is their difference.
Frequently asked questions
What is the correct answer to this question?
62
Why is this the correct answer?
The symmetric difference A △ B contains elements that belong to exactly one of the two sets. Its cardinality is n(A △ B) = n(A) + n(B) − 2n(A ∩ B). Since the intersection has size zero, the sets are disjoint and n(A △ B) = 28 + 34 − 0 = 62. Options 28 and 34 count only one set, while 6 is their difference.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
